It is possible that overheating will change the composition of some lead alloys. Tin, if present, will oxidize, thereby changing the alloy. A tin-lead alloy melts/solidifies at a lower temperature than pure lead. Here is a phase diagram for lead tin, it shows the melting temperatures http://www2.umist.ac.uk/material/research/intmic/phase/pbsndiag.htm
Adding flux to lead alloys will reverse tin oxidation.
I've used shot before and had no problems with it, if I got it for free I'd definitely use it. Some shot contains arsenic, which increases hardness. This site has more info about lead http://www.lasc.us/myweb/CastBulletNotes.htm